Existence and approximation results to the Cauchy problem for a class of differential-algebraic equations. (English) Zbl 0772.34003

Schneider, K. R.

Z. Anal. Anwend. 10, No. 3, 375-384 (1991).

Summary: For a class of differential-algebraic equations arising for example in modelling electrical circuits conditions are derived which ensure the existence of a unique solution of the Cauchy problem on any finite interval and its computation by means of a wave form relaxation algorithm in case of a large system. The solution concepts is understood in the sense of Carathéodory.

MSC:

34A09	Implicit ordinary differential equations, differential-algebraic equations
34A34	Nonlinear ordinary differential equations and systems
65J99	Numerical analysis in abstract spaces
94C05	Analytic circuit theory
65L05	Numerical methods for initial value problems involving ordinary differential equations
37-XX	Dynamical systems and ergodic theory

Keywords:

differential-algebraic equations; electrical circuits; existence; Cauchy problem; computation; wave form relaxation algorithm; large system